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3.7 Numerical methods (A-level only)

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Question 95

A researcher is monitoring the concentration of a specialized catalyst, PPP mg/L, within a chemical bioreactor. The concentration ttt minutes after the reaction commences is modelled by the equation

P=480e0.12t2e0.12t+3,t≥0, t∈R P = \frac{480e^{0.12t}}{2e^{0.12t} + 3}, \quad t \ge 0, \ t \in \mathbb{R} P=2e0.12t+3480e0.12t​,t≥0, t∈R

According to this model:

a.

Determine the concentration of the catalyst at the instant the reaction begins.

[2]
b.

Calculate the time ttt at which the concentration reaches 160 mg/L, giving your answer to 2 decimal places.

[3]
c.

Explain why, according to this model, the concentration of the catalyst can never reach 250 mg/L.

[2]

3.7 Numerical methods (A-level only) Questions

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